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A survey of constraint qualifications with second-order properties in nonlinear optimization

Gabriel Haeser(ghaeser***at***ime.usp.br)
Alberto Ramos(albertoramos***at***ufpr.br)

Abstract: In this paper we discuss recent developments in first- and second-order constraint qualifications that imply second-order optimality conditions. In the first-order case, we are particularly interested in conditions that ensure the validity of second-order necessary optimality conditions that can be checked with a single Lagrange multiplier and defined in terms of positive semidefiniteness on a subspace, due to its connections with global convergence of second-order algorithms. In the second-order case, we discuss necessary and sufficient conditions to ensure the validity of second-order optimality conditions.

Keywords: Nonlinear optimization, Constraint qualifications, Global convergence, Second-order optimality conditions

Category 1: Nonlinear Optimization


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Entry Submitted: 01/07/2018
Entry Accepted: 01/07/2018
Entry Last Modified: 01/07/2018

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